Questions from General Calculus

Q: Set Y1 = ex and use your calculator’s derivative command to specify

Set Y1 = ex and use your calculator’s derivative command to specify Y2 as the derivative of Y1. Graph the two functions simultaneously in the window [-1, 3] by [-3, 20] and observe that the graphs ove...

Q: Calculate values of (10x – 1)/x for small values

Calculate values of (10x – 1)/x for small values of x, and use them to estimate d/dx (10x) |x=0 . What is the formula for d/dx (10x)?

Q: Compute the given derivatives with the help of formulas (1)–(

Compute the given derivatives with the help of formulas (1)–(4). (a) d/dx (ex) |x=e (b) d/dx (ex) |x=1/e

Q: Write each expression in the form ekx for a suitable constant k

Write each expression in the form ekx for a suitable constant k. (e2)x, (1/e)x

Q: Write each expression in the form ekx for a suitable constant k

Write each expression in the form ekx for a suitable constant k. (e3)x/5, (1/e2)x

Q: Write each expression in the form ekx for a suitable constant k

Write each expression in the form ekx for a suitable constant k. (1/e3)2x, e1-x * e3x-1

Q: Ten grams of a radioactive material disintegrates to 3 grams in 5

Ten grams of a radioactive material disintegrates to 3 grams in 5 years. What is the half-life of the radioactive material?

Q: Find the equation of the tangent line to the curve y =

Find the equation of the tangent line to the curve y = (x - 2)5 (x + 1)2 at the point (3, 16).

Q: Let A(t) = 5000e0.04t be the balance

Let A(t) = 5000e0.04t be the balance in a savings account after t years. (a) How much money was originally deposited? (b) What is the interest rate? (c) How much money will be in the account after 10...

Q: Pablo Picasso’s Angel Fernandez de Soto was acquired in 1946 for a

Pablo Picasso’s Angel Fernandez de Soto was acquired in 1946 for a postwar splurge of $22,220. The painting was sold in 1995 for $29.1 million. What yearly rate of interest compounded continuously did...